[14/24] feat: add Application behavior for managing supervision trees

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Summary

Add Erlang-style application module for packaging and managing supervision trees as units.

Features

• Application trait for defining applications with:
  • start() - create and start supervision tree
  • prep_stop() - cleanup hook before stopping
  • stopped() - hook after termination
• Global registry of running applications
• Functions:
  • start::<A>(config) - start an application
  • stop::<A>() - stop an application
  • is_running::<A>() - check if running
  • whereis::<A>() - get root supervisor PID
  • which_applications() - list all running apps
  • call::<A>(msg) - send message to supervisor
  • get_handle::<A>() - get supervisor handle

Usage

struct MyApp;

impl Application for MyApp {
    type Config = i32;

    fn name() -> &'static str { "my_app" }

    fn start(config: Self::Config) -> Result<GenServerHandle<Supervisor>, ApplicationError> {
        let spec = SupervisorSpec::new(RestartStrategy::OneForOne)
            .child(ChildSpec::worker("counter", move || {
                Counter::new(config).start(Backend::Async)
            }));
        Ok(Supervisor::start(spec))
    }
}

// Start the application
let pid = application::start::<MyApp>(42)?;

// Check status
assert!(application::is_running::<MyApp>());

// Stop the application
application::stop::<MyApp>().await?;

Test plan

• All 164 tests pass
• Clippy clean
• New application tests for start/stop, multiple apps, call, get_handle

🤖 Generated with Claude Code

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Reorganizing PR sequence for coherent implementation order. This content will be included in the new PR series.